Free street parking is available anywhere south of 31st Street. Watch the one-ways and you'll be good to go. Be on the lookout for green signs indicating permit required - stay away from there.
There is plenty of metered (pay at a central station on each block) parking throughout Uptown, primarily on Hennepin Avenue, Lagoon Avenue, and Lake Street. Sections of metered parking along 31st Street on either side of Hennepin Avenue, along 28th Street west of Hennepin, and in select other locations. Some stalls are limited to 15 minutes while others don’t allow you to park there during rush hour, so read the signs. And yes, they will tow you. Parking pay machines accept cash, limited coin, and credit cards.
Calhoun Square Parking Ramp
Enter off of 31st Street between Fremont Avenue and Girard Avenue. This ramp is one of the largest parking facilities in the Uptown area. It is conveniently located in the heart of Uptown and has a skyway connection to Calhoun Square. See rates here